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If you don't want to use any online tools. You can download a few different browsers to your own computer, as most developers will have a few anyway. Perhaps try Mozilla Firefox, Internet Explorer, Opera Browser and Google Chrome. You can then change your screen resolution to check the site at different sizes.

leeham, why do that (and go to all that trouble) when you could simply resize the browser window to 1024x768 or 800x600 to see (effectively) how a website would look in a maximized browser window at that native resolution?

ie is the most forgiving browser so best not to do your websites using ie, opera seems to show a lot more errors and is very unforgiving but has a real bad tendency to cache everything so when you do changes it seems as though nothing has changed, ie you do a normal refresh and it will draw most of your page out of your cache, so you got to remember to hard refresh, CTRL + F5.

You really don't want to use the most forgiving browser to do a website, you need to see where you have messed up, a professional website does not have, "This website is best viewed in etc", if you have to put that in it would be best to learn more about developing websites before you actually start putting them online.